Problem: Simplify the following expression: $r = \dfrac{-2q - 7}{7q - 1} - \dfrac{5q - 1}{7q - 1}$
Explanation: Since the expressions have the same denominator we simply subtract the numerators: $r = \dfrac{-2q - 7 - (5q - 1)}{7q - 1}$ Distribute the negative sign: $r = \dfrac{-2q - 7 - 5q + 1}{7q - 1}$ Combine like terms: $r = \dfrac{-7q - 6}{7q - 1}$